An atomic force microscope is a device used to produce images of surface topography (and other sample characteristics) based on information obtained from rastering a sharp probe on the end of a cantilever relative to the surface of a sample. Deflections of the cantilever, or changes in its oscillation which are detected while rastering correspond to topographical (or other) features of the sample. Deflections or changes in oscillation are typically detected by an optical lever arrangement whereby a light beam is directed onto a cantilever in the same reference frame as the optical lever. The beam reflected from the cantilever illuminates a position sensitive detector (PSD). As the deflection or oscillation of the cantilever changes, the position of the reflected spot on the PSD changes, causing a change in the output from the PSD. Changes in the deflection or oscillation of the cantilever typically trigger a change in the vertical position of the cantilever base relative to the sample, in order to maintain the deflection or oscillation at a constant pre-set value. This feedback generates the image from the atomic force microscope, called an AFM image.
Atomic force microscopes can be operated in a number of different imaging modes. In contact mode, the tip of the cantilever is in constant contact with the sample surface. In oscillatory modes, the tip makes no contact or only intermittent contact with the surface.
FIG. 1 shows one prior art approach to the use of actuators in an atomic force microscope. A sample 1 is attached to a z-actuator 2. The base 7 of a flexible cantilever 6 is attached to xy-actuator 8 which is attached to a head frame 9 (“xy” here represents that the actuator moves in the horizontal XY plane, and “z” represents that the actuator moves in the vertical direction, “X” and “Y” and “Z” being mutually orthogonal directions). The xy-actuator 8, combined with the z-actuator 2, provides relative motion between the probe 5 and the sample 1 in all three dimensions. The z-actuator 2 is supported by a structure 3 attached to the frame 4 of the instrument. The cantilever 6 deflects in response to interactions between the probe 5 and the sample 1. This deflection is measured by a PSD 10. The output of the PSD 10 is collected by the controller 11. Typically, the controller 11 performs some processing of the signal, extracting quantities such as the cantilever deflection, amplitude, phase or other parameters. These values are often displayed on a display device 12. Furthermore, the controller 11 can operate a feedback loop that in turn varies the relative position of the base 7 of the cantilever 6 and the sample 1 in response to sample characteristics.
Accurate characterization of a sample by an atomic force microscope is often limited by the ability of the atomic force microscope to move the base of the cantilever vertically in the Z direction relative to the sample surface at a rate sufficient to characterize the sample accurately while scanning in either the X or Y direction.
This movement rate is often expressed in terms of bandwidth. The bandwidth required depends on the desired image size (in pixels) and acquisition rate of each pixel. Table 1 below shows the bandwidth required for various imaging scenarios. For example, completing a 256×256 pixel image in one second requires a bandwidth of 131 kHz.
TABLE 1Closed loop bandwidths (BW) required forhigh speed atomic force microscope imaging.Closed Loop bandwidths Required (kHz)Images/Second1282 Pixels2562 Pixels5122 Pixels0.11.646.552.40.23.313104116.4131524581.93282620101646555240
In order to accurately measure the height of all features, both large and small, on a sample surface, the z-actuator must have the ability to provide relative motion between the base of the cantilever and sample surface over a large range of heights, i.e., it must have large vertical travel. The z-actuator can be a scanning tube in many conventional Atomic force microscopes. In other microscopes, such as the Asylum Research MFP-3D atomic force microscope, the z-actuator is a flexure. The parts must be large enough to move the cantilever up and down sufficiently to measure even the largest surface features.
The range of actuation of many actuators scales with the physical dimensions of the device. This is certainly the case with piezo actuators. For example, in the case of commercially available piezo stack actuators from TOKIN Incorporated, the maximum travel range is nominally 4.6 um, 9.1 um and 17.4 um for stacks having respective lengths of 5 mm, 10 mm and 20 mm. Accordingly, a by-product of increasing the travel range, is that actuators become more massive. These more massive actuators move more slowly.
One way of characterizing the speed of actuator movement is the resonant frequency of the actuator. The piezo stacks mentioned above have resonant frequencies of roughly 261 kHz, 138 kHz and 69 kHz respectively. It may be noted that the piezo material used in these three stacks is the same. The change in resonant frequency is primarily due to the different sizes and therefore masses.
The quoted resonant frequencies are for the bare stacks. Attaching these bare stacks to a support structure or incorporating them in a flexure will substantially further reduce the resonant frequency. Furthermore, attaching any mass to the piezo will further reduce the resonant frequency.
In practice, this means that the actuator may not be able to move either the sample or the base of the cantilever rapidly enough to track the surface accurately. This can lead to either the sample and/or probe being damaged, or to the reproduction of the surface topography being less accurate. In order to avoid these consequences, an atomic force microscope operator will typically decrease the scan rate in the X and Y directions until the z-actuator can accommodate the topographical variations in the sample.
Typically, an atomic force microscope operator begins by increasing the feedback loop gain to increase the response of the z-actuator. However, at some point, the z-actuator will begin to resonate and that resonant motion will create parasitic oscillations in the actuator support structure and even change the phase of the response of the actuator to inputs. These parasitic oscillations and phase changes reduce the performance of the instrument and the quality of the images and other data produced.
The actuation scheme depicted in FIG. 1 is representative of a great number of actuation schemes commonly used to provide relative movement between a tip and sample. This may provide a useful model for analyzing what happens when the atomic force microscope operator increases the feedback loop gain to increase the response of the z-actuator. Increasing the feedback loop gain increases the extension of the z-actuator 2 in the vertical or Z direction. This increased extension, however, results in an increased reaction force on the support structure 3.
FIG. 2 constitutes the lower-left segment of FIG. 1, showing this in more detail. In FIG. 2, as in FIG. 1 the sample 1 is supported by the z-actuator 2. FIG. 2—Reaction Forces shows the z-actuator 2 extending and moving the sample 1 a distance ΔZsam. This movement requires a force Fsam is exerted on the sample to cause acceleration of the sample. Newton's second law implies there is a corresponding reaction force Fsup exerted on the support structure 3. This reaction force will cause some deflection in the support structure, ΔZsup. Flexing of the support structure leads to ringing, reduced motion of the sample (ΔZsam) and generally reduced bandwidth of sample actuation.
One approach to overcoming the consequences of speeding up image acquisition has been to allow the cantilever error signal to vary over the scan range, but to keep the average value at a setpoint (Albrecht and Quate). With this approach, the job of the feedback loop is made much easier, allowing faster scanning. However, large variations in the error parameter using this technique may have detrimental effects, including but not limited to tip dulling or damage and sample damage.
Another approach has been to use “nested” actuators. A large, relatively long-range and slow actuator is used along with a small, short range but much faster actuator. This allows images to be obtained at higher speeds because the small fast actuator can accommodate small surface variations while the large actuator takes care of the gross height variations over the entire XY scan range. One example of this approach is the zinc oxide piezo actuators integrated into cantilevers by Sulchek et al. and Rogers et al. These actuated cantilevers, together with the typical actuators controlling the distance between the cantilever base and the sample surface, allows the effective distance between the base of the cantilever and the surface of the sample to be maintained constant at the same time that the cantilever probe characterized the sample. Using these cantilevers, a bandwidth of 38 kHz has been demonstrated.
The actuated cantilever approach raises some difficulties. Combining fast and slow feedback loops is not always trivial. Tuning two feedback loops is significantly more time consuming and problematic than tuning a single loop. The scan speed gain is often rather moderate considering the complexity required of the operator. Combining the final data to obtain an accurate characterization of the sample is also more complicated and prone to instrumentation errors and artifacts. Actuated cantilevers are necessarily quite stiff, making imaging of soft samples problematic. Imaging in fluids, one of the strengths of the atomic force microscope, is difficult to implement with actuated cantilevers because of the requirements for electrical contacts directly to the cantilever. Changing the sample to one with a mass different than the design value of the actuated cantilever may seriously degrade its ability to overcome the effects of fast image acquisition. Finally, even actuated cantilevers have a resonance, a property which of course induces parasitic oscillations and phase shifts and therefore reduces data quality and leads to cantilever and/or sample damage.
Another approach to minimizing parasitic oscillations and phase shifts while speeding up atomic force microscope image acquisition is to construct the actuators in a recoilless, balanced arrangement where there is essentially no momentum transferred to the frame of the instrument. Typically, this arrangement includes the use of additional damping material to correct for any small discrepancies in the design, construction or material properties of the balanced actuators. The balanced actuator approach has been used by Cleveland et al., Ando et al. and Massie. A weakness is that the system is an open loop system. If, for example, the actuated mass changes, as is common when the sample is changed, or if the piezo sensitivity changes, as commonly happens with age, the balancing will become less and less effective.
FIG. 3 depicts the balance actuator approach. As with FIG. 1, a sample 1 is attached to a z-actuator 2 and the z-actuator is supported by a support structure 3 attached to the frame of the instrument 4. In this case however, there is a secondary z-actuator 13 positioned below the support structure 3 and an optional mass 14 attached to the secondary z-actuator 13. In addition, there can be a variable gain drive 15 for the secondary actuator. The z-actuator 2, as well as the secondary z-actuator 13 with variable gain drive 15 are driven with similar (or the same) feedback signal. The gain provided by variable gain drive 15 and the mass 14 are chosen so that the momentum transferred to the support structure 3 is substantially zero. Specifically, the force exerted on the support structure 3 by the base of the z-actuator 2 is equal and opposite to that exerted by the base of the secondary z-actuator 13.
Analogous operations can also be accomplished in a number of other ways, including using balanced flexures. See U.S. Pat. Nos. 6,459,088 B1 and 6,323,483 B1 for a host of methods all with the goal of reducing the momentum transferred to the support to essentially zero. This method has also been used with a number of variations by the group of Ando.
The balanced actuator approach of FIG. 3 is an open-loop system in which the design is carefully focused on balancing opposed actuators and thereby avoiding the excitation of resonances in the support structure. An open loop system however presents disadvantages. Experimental results of systems such as that in FIG. 3 have shown that if the mass of the sample 1 changes, as commonly occurs in atomic force microscope operation, the balancing condition will no longer be met and momentum will be transferred to the support structure 3 by the movements of actuators 2 and 13. This in turn induces the very resonances the approach seeks to avoid. Furthermore, the sensitivity of actuators can change over time or in response to environmental conditions, and this too also introduces these problems. Finally, the open loop, balanced approach requires very thorough manufacturing control.
The modifications in the balanced actuator approach recently proposed by Ando, attempt to overcome these disadvantages by including a model of the drive or “dummy” actuator (as they referred to it in their work) in the drive of the otherwise open loop actuators 2 and 13. However this solution has its own disadvantages when the behavior of either of the actuators begins to deviate from the “dummy” actuator. Ando's modifications provide no mechanism to measure and automatically correct the motion of the compensating system for the new actuator behavior.
A recent approach to the problem of speeding up image acquisition without inducing parasitic oscillations and phase shifts is that of Kodera et al. They have proposed a method of damping the resonances of a balanced scanner based on Q-control ideas. Their method introduces a “mock scanner” into the drive circuit for the z-actuator which in turn allows the phase of the drive to be adjusted to reduce the amplitude of the actuator resonances. This approach suffers from the limitation that the behavior of the actuator has to be preprogrammed and if its characteristics change, the damping effects will no longer function optimally, if at all.